Additional Results on Oversmoothing and Empirical Performance
Dear reviewers,
We would like to thank all reviewers again for your thoughtful reviews and valuable feedback. We have obtained additional empirical results to clarify the impact of oversmoothing on the model’s performance. We summarize our results below.
In Figure 7 (Left) in the rebuttal PDF, our NeuTRENO BERT finetuned on the SQUAD question answering task [1] yields better accuracy than the baseline BERT finetuned on the same task (81.39 exact match score and 88.62 F1 score vs. 80.77 exact match score and 88.12 F1 score). In Figure 7 (Right) in the rebuttal PDF, our NeuTRENO SimCSE, after finetuned on the STS-12 semantic textual similarity task [2], gains a significant improvement over the baseline SimCSE [3], which is also finetuned on the same task (77.32% vs. 75.29% Spearman's correlation. Here, the higher correlation, the better). These results indicate that reducing cosine similarity between tokens in the trained transformer-based models leads to better empirical performance.
We would also like to provide additional evidence that oversmoothing is indeed an issue for vision transformers (ViT). Indeed, the oversmoothing in ViT has been verified and investigated in existing works. In particular, [4] observes that the performance of ViT quickly saturates as more layers are added to the model. Moreover, experiments in [4] show that the 32-layer ViT underperforms the 24-layer ViT, indicating the difficulty of ViTs in gaining benefits from deeper architectures. The authors point out that oversmoothing results in this phenomenon by causing the token representations to become identical when the model grows deeper. Based on this observation, they propose a cross-head communication method that helps enhance the diversity of both token representations and attention matrices.
Furthermore, it has been shown in [5] that the training of ViT models encounters instability with greater depths. [6] proposes that this instability arises from the oversmoothing, where token representations for patches within an image become progressively alike as the model's depth increases. In an effort to explain this issue, [7] finds out that self-attention acts as a low-pass filter, which smoothens the token representations in ViTs. This leads to the proposal of the FeatScale method [7], which regulates feature frequencies, whether low or high, to counteract the consequences of oversmoothing.
Different from existing works, in our paper, we theoretically prove the oversmoothing phenomenon via the variational denoising framework that we develop. Our proposed NeuTRENO method helps mitigate the oversmoothing issue and improves the performance of the ViT baselines (DeiTs), as well as other baseline transformer-based models. We also empirically demonstrate that NeuTRENO not only reduces the cosine similarity between token representation (See Figure 1 in the main text and Figure 7) but also the redundancy in attention maps between layers (See Figure 5 in Appendix G2). Finally, we show that NeuTRENO is complementary to existing methods, including FeatScale [7] (See Table 1 and Table 7 in our paper).
We would be happy to do any follow-up discussion or address any additional comments.
**References**
[1] Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. “SQuAD: 100,000+ questions for machine comprehension of text”. EMNLP, 2016.
[2] Eneko Agirre, et al. “SemEval-2012 task 6: A pilot on semantic textual similarity.” SemEval, 2012.
[3] Gao, T., Yao, X., and Chen, D. "SimCSE: Simple contrastive learning of sentence embeddings". EMNLP, 2021.
[4] Daquan Zhou, et al. “Deepvit: Towards deeper vision transformer”. arXiv, 2021.
[5] Touvron Hugo, et al. "Going deeper with image transformers." ICCV, 2021.
[6] Chengyue Gong, et al. “Vision transformers with patch diversification”. arXiv, 2021.
[7] Wang Peihao, et al. "Anti-oversmoothing in deep vision transformers via the fourier domain analysis: From theory to practice." ICLR, 2022.